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MFP1501 Assignment 2 Due 18 June 2024
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MFP1501 Assignment 2 Due 18 June 2024
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MFP1501ASSIGNMENT 2
Instructions
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assessment after scanning.
Question 1
Jacob and Willis (2003) outline hierarchical phases through which multiplicative
thinking develops, which include one-to-one counting, additive composition, many-to-
one counting, and multiplicative relations. Discuss each phase to show how best you
understand it. N.B. It should not be the same. Be creative.
One-to-one counting: The Explorer Phase
In this phase, children are like explorers setting foot on a new land of numbers. They see
each number as a unique landmark, counting them one by one. Just as explorers mark their
path with each step, these learners mark their understanding with each counted object.
However, much like explorers initially focus on individual trees rather than the forest, these
children perceive numbers individually rather than seeing the relationships between them. To
guide them into this new territory, educators act as experienced navigators, showing them
that rearranging the landscape doesn't change its essence. Through engaging activities,
children discover that no matter how the objects are arranged, the total count remains the
same, akin to finding different routes to the same destination.
Additive composition: The Architect Phase
As children advance, they transition into the role of architects, constructing their
understanding of numbers like builders laying bricks. They now grasp that numbers can be
rearranged without altering the total, similar to designing a building with interchangeable
components. Yet, their focus remains on the individual components rather than the structure
as a whole. Educators serve as mentors, guiding them to see beyond the bricks to the
blueprint that unites them. Through hands-on activities, children learn to see the relationships
between groups, shifting from simply adding components to understanding the
interconnectedness of the whole structure.
Many-to-one counting: The Conductor Phase
Now, children step into the role of conductors, orchestrating the symphony of numbers with
finesse. Like a skilled conductor leading an ensemble, they can simultaneously keep track of
multiple elements, guiding them towards harmony. They understand that numbers can be
grouped and counted efficiently, much like orchestrating different sections of an orchestra to
create a unified melody. However, they may still struggle to switch between different
compositions, much like a conductor navigating between musical pieces. Educators act as
maestros, teaching children to seamlessly transition between different numerical
, arrangements, enabling them to conduct their mathematical symphony with confidence and
precision.
Multiplicative relations: The Mastermind Phase
In this final phase, children ascend to the role of masterminds, wielding their deep
understanding of numbers with expertise. Like master strategists on a chessboard, they
anticipate the consequences of each numerical move, seeing the interconnectedness of every
piece. They recognize that every numerical scenario involves three key elements, akin to
analyzing the intricate dynamics of a complex strategy. Educators act as mentors, guiding
children to unlock the full potential of their numerical prowess. Through engaging challenges
and explorations, children develop a profound understanding of the relationships between
numbers, enabling them to navigate the mathematical landscape with mastery and finesse.
Question 2
In the Foundation Phase, multiplication is commonly introduced as repeated addition,
that is, situations where several groups of the same size need to be added together.
We usually ask questions such as: “How big is each group or how many groups?
Provide five examples which are different from those in the study guide.
Shopping Spree in Africa Mall:
Kaylin went shopping and bought 3 packs of gum, with 4 gums in each pack. How many
gums did Kaylin buy in total?
A Pizza Party at Rocklands:
At a party, there are 5 pizzas, and each pizza is cut into 8 slices. How many pizza slices are
there in total?
Bookshelves:
A library has 6 shelves, and each shelf can hold 10 books. How many books can the library
hold in total?
Candy Distribution:
There are 8 bags of candies, and each bag contains 12 candies. How many candies are
there in total?
Joubiez School Supplies:
Ms. Jacobs bought 9 packs of markers, with 6 markers in each pack. How many markers did
the teacher buy in total?
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